Difference between revisions of "Manuals/calci/BESSELY"

Revision as of 00:11, 2 December 2013

BESSELY(x,n)

This function gives the value of the modified Bessel function.
Bessel functions is also called Cylinder Functions because they appear in the solution to Laplace's equation in cylindrical coordinates.
Bessel's Differential Equation is defined as: $x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+(x^{2}-\alpha ^{2})y=0$

where $\alpha$ is the arbitrary complex number.

But in most of the cases $\alpha$ is the non-negative real number.
The solutions of this equation are called Bessel Functions of order $n$ .
The Bessel function of the second kind $Yn(x)$ and sometimes it is called Weber Function or the Neumann Function..
The Bessel function of the 2nd kind of order can be expressed as: $Yn(x)=\lim _{p\to n}{\frac {J_{p}(x)Cos(p\pi )-J_{-p}(x)}{Sin(p\pi )}}$
where Jn(x) is the Bessel functions of the first kind.
This function will give the result as error when 1.x or n is non numeric2. n<0, because n is the order of the function

@@ Line 10: / Line 10: @@
 *The solutions of this equation are called Bessel Functions of order <math>n</math>.
 *The Bessel function of the second kind <math>Yn(x)</math> and sometimes it is called Weber Function or the Neumann Function..
-*The Bessel function of the 2nd kind of order  can be expressed as: <math>Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J-_p(x)}{Sin(p\pi)}</math>
+*The Bessel function of the 2nd kind of order  can be expressed as: <math>Yn(x)= \lim_{p \to n}\frac{J_p(x)Cos(p\pi)- J_{-p}(x)}{Sin(p\pi)}</math>
 *where Jn(x) is the Bessel functions of the first kind.
 *This function will give the result as error when 1.x or n is non numeric2. n<0, because n is the order of the function